Solve for Unknown Angles — Transversals

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New York State Common Core Math Geometry, Module 1, Lesson 7

Worksheets for Geometry

Student Outcomes

  • Students review formerly learned geometry facts and practice citing the geometric justifications in anticipation of unknown angle proofs.

Solve for Unknown Angles — Transversals


Opening Exercise

Use the diagram at the right to determine 𝑥 and 𝑦. 𝐴𝐵 and 𝐶𝐷 are straight lines.
𝑥 =
𝑦 =
Name a pair of vertical angles:
Find the measure of ∠𝐵𝑂𝐹. Justify your calculation.


Given line 𝐴𝐵 and line 𝐶𝐷 in a plane (see the diagram below), a third line 𝐸𝐹 is called a transversal if it intersects 𝐴𝐵 at a single point and intersects 𝐶𝐷 at a single but different point. Line 𝐴𝐵 and line 𝐶𝐷 are parallel if and only if the following types of angle pairs are congruent or supplementary.

  • Corresponding angles are equal in measure.
  • Alternate interior angles are equal in measure.
  • Same-side interior angles are supplementary.


An __________ is sometimes useful when solving for unknown angles. In this figure, we can use the auxiliary line to find the measures of ∠𝑒 and ∠𝑓 (how?) and then add the two measures together to find the measure of ∠𝑊. What is the measure of ∠𝑊?

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